364 



Murray Eden 



edge. This lime, of the six three-celled configurations obtained by adjoining 

 a cell to an open edge, four are isomorphic to one of two three-celled configura- 

 tions, and two to the other. Thus, the probability of the first three-celled 

 configuration is 0.67 and the other 0.33. This procedure can be carried out 

 indefinitely, in each case assigning equal weight to each open edge and adjoining 

 a single cell at a time. 



Table II. Number of Configurations in Each Array 



While there is no biological organism that exhibits this pattern of growth, 

 it has certain features in common with some tissue cultures, bacterial colonies 

 or tumors, in that the cells are more or less undifferentiated. Growth in such 



"^-12 7^-10 7rM2 7r^I2 7r-I2 7r=l2 7M4 



(1) ^ (I) ^ (2) Ug (1) 4^ (I) ^^ (2) ^ (3) d^ 

 0I1S9 0.0883 0.0817 0.0761 0.0594 0.0511 0.0250 



(1) n^ Ocfim '" 



7r=I4 Tr=l4 



'^' a&n <«' crrxfl <» ^ '^' Bifi 



0.0229 0.0203 0.0194 0.0125 0.0111 0.0104 0.00555 



TT^U 



(I) 



6- ARRAY 



Fig. 1 



biological objects has no preferential direction except that it is peripheral, 

 a condition due most likely to the fact that diffusion of nutrient is too slow to 

 permit any large number of cell divisions in the interior of the growth. 



Exact computations have been carried out for the probability associated 

 with each A'-configuration up to k = 8. As before, computations for k > S, 

 while easily performed in principle, are prohibitively time-consuming. The 

 configurations for k = 6, 7, 8 and their associated probabilities are assembled 

 in Fig. 1, 2, 3. 



An unanticipated property of the particular generating function employed 

 was revealed as a consequence of these exact computations. It will be observed 

 in Fig. 1 to 3 that configurations have been grouped so that each different 

 value of probability is recorded next to a single prototype configuration. 



